{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy import *\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "sns.set(context=\"notebook\", style='whitegrid', palette=\"dark\")\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Regression with one variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = pd.read_csv('ex1data1.txt', names = ['population', 'profit'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## check the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "   population   profit\n0      6.1101  17.5920\n1      5.5277   9.1302\n2      8.5186  13.6620\n3      7.0032  11.8540\n4      5.8598   6.8233",
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>population</th>\n      <th>profit</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>6.1101</td>\n      <td>17.5920</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>5.5277</td>\n      <td>9.1302</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>8.5186</td>\n      <td>13.6620</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>7.0032</td>\n      <td>11.8540</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>5.8598</td>\n      <td>6.8233</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "metadata": {},
     "execution_count": 26
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.1 plottint the Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {}
    }
   ],
   "source": [
    "plt.scatter(data['population'], data['profit'],s=10)\n",
    "plt.xlabel('Population of city in 10,000s')\n",
    "plt.ylabel('Profit in $10,000s')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2.2 Gradient Descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calcCost(x, y, theta):\n",
    "    temp = np.power(((x * theta.T) - y), 2) \n",
    "    return np.sum(temp) / (2 * len(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "data.insert(0, 'Ones', 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "cols = data.shape[1]\n",
    "x = data.iloc[:,0:cols-1]\n",
    "y = data.iloc[:,cols-1:cols]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "   Ones  population\n0     1      6.1101\n1     1      5.5277\n2     1      8.5186\n3     1      7.0032\n4     1      5.8598",
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>Ones</th>\n      <th>population</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>1</td>\n      <td>6.1101</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>1</td>\n      <td>5.5277</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>1</td>\n      <td>8.5186</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>1</td>\n      <td>7.0032</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>1</td>\n      <td>5.8598</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "metadata": {},
     "execution_count": 31
    }
   ],
   "source": [
    "x.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "    profit\n0  17.5920\n1   9.1302\n2  13.6620\n3  11.8540\n4   6.8233",
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>profit</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>17.5920</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>9.1302</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>13.6620</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>11.8540</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>6.8233</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "metadata": {},
     "execution_count": 32
    }
   ],
   "source": [
    "y.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta = np.matrix(np.array([0,0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "matrix([[0, 0]])"
     },
     "metadata": {},
     "execution_count": 37
    }
   ],
   "source": [
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "((97, 2), (97, 1), (1, 2))"
     },
     "metadata": {},
     "execution_count": 38
    }
   ],
   "source": [
    "x.shape, y.shape, theta.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "profit    32.072734\ndtype: float64"
     },
     "metadata": {},
     "execution_count": 39
    }
   ],
   "source": [
    "calcCost(x,y,theta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 批量梯度下降"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradientDescent(X, y, theta, alpha, iters):\n",
    "    temp = np.matrix(np.zeros(theta.shape))\n",
    "    parameters = int(theta.ravel().shape[1])\n",
    "    cost = np.zeros(iters)\n",
    "    \n",
    "    for i in range(iters):\n",
    "        error = (X * theta.T) - y\n",
    "        \n",
    "        for j in range(parameters):\n",
    "            term = np.multiply(error, X[:,j])\n",
    "            temp[0,j] = theta[0,j] - ((alpha / len(X)) * np.sum(term))\n",
    "            \n",
    "        theta = temp\n",
    "        cost[i] = calcCost(X, y, theta)\n",
    "        \n",
    "    return theta, cost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha = 0.01\n",
    "iters = 1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "matrix([[-3.24140214,  1.1272942 ]])"
     },
     "metadata": {},
     "execution_count": 47
    }
   ],
   "source": [
    "g, cost = gradientDescent(x, y, theta, alpha, iters)\n",
    "g"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "profit    4.515956\ndtype: float64"
     },
     "metadata": {},
     "execution_count": 48
    }
   ],
   "source": [
    "calcCost(x,y,g)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 864x576 with 1 Axes>",
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     },
     "metadata": {}
    }
   ],
   "source": [
    "x = np.linspace(np.min(data['population']), np.max(data['population']), 100)\n",
    "f = g[0, 0] + (g[0, 1] * x)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(12,8))\n",
    "ax.plot(x, f, 'r', label='Prediction')\n",
    "ax.scatter(data['population'], data['profit'], label='Traning Data')\n",
    "ax.legend(loc=2)\n",
    "ax.set_xlabel('population')\n",
    "ax.set_ylabel('profit')\n",
    "ax.set_title('Predicted Profit vs. Population Size')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "matrix([[-3.24140214,  1.1272942 ]])"
     },
     "metadata": {},
     "execution_count": 62
    }
   ],
   "source": [
    "g"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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beYlwAAAAENKO4pUNAQAAIBHSjiOkAQAAIELaYVwjDQAAAImQdhwn0gAAABAh7TBOpAEAACAR0o7jRBoAAAAipB3GiTQAAAAkQtpxJpMkQhoAAKCoI6QdxYk0AAAAREg7jBdkAQAAgERIO8xkNhPSAAAAIKQdZ5LNajV6BAAAAAxGSDuIZ+0AAACAREg7jmukAQAAIELaYZxIAwAAQCKkHceJNAAAAERIO44TaQAAAIiQdhjPIw0AAACJkHYcIQ0AAAAR0g7jjw0BAAAgEdKO40QaAAAAIqQdxok0AAAAJELaYSazmZcIBwAAACHtMC7tAAAAgAhph3FpBwAAACRC2nGcSAMAAECEtOM4kQYAAIAIaYfxyoYAAACQCGnHEdIAAAAQIe0w/tgQAAAAEiHtOE6kAQAAIELaYZxIAwAAQCKkHWcySSKkAQAAijpC2kG8RDgAAAAkJ4d0ZGSk+vbtqy5duuiNN9645/4jR46oX79+6ty5s15++WWlpaU5c07u4NIOAAAAyIkhHR0drYkTJ+qTTz7R8uXLdfjwYW3cuDHLY1588UW98sorWrNmjWw2mxYsWOCsObmG55EGAACA5MSQXrt2rbp166agoCC5urpq2rRpatiwof3+8+fP6/bt22rUqJEkqW/fvlq9erWz5uQiQhoAAABODOkzZ84oPT1do0aNUq9evTR37lz5+vra7798+bJKly5t/7x06dK6dOmSs+bkGp61AwAAAJITQzo9PV3bt2/X1KlTtWDBAh06dEgRERH2++8XoyaTyVlzcg+XdgAAAEBODGl/f3+FhobKz89PHh4eat++vQ4ePGi/PzAwUFevXrV/fuXKFQUEBDhrTq7hRBoAAACSE0O6bdu22rJli+Li4pSenq7Nmzerbt269vvLlSsnd3d37d27V5K0ZMkStWrVyllzcg8n0gAAAJATQ7phw4YaPXq0Bg8erG7duqls2bLq16+fxowZo0OHDkmS3n33Xb311lvq2rWrbt26pWHDhjlrTq7hRBoAAACSZLIVwCpMTk5WVFSU6tWrJ3d39zz92cuHDNTVnw9p5H+O5OnPBQAAQN57UHfyyoaO4kQaAAAAIqQdZjKbuUYaAAAAhLSjTCaTbFar0TMAAABgMELaUTxrBwAAAERIO4xn7QAAAIBESDuOE2kAAACIkHaY2cVF1rQ0o2cAAADAYIS0g7wCApV46SJ/cAgAAFDEEdIOKh5cXtbUVCVdvmz0FAAAABiIkHZQ8eDykqT48+cMXgIAAAAjEdIOsof0uWiDlwAAAMBIhLSDMkM69tdTBi8BAACAkQhpB3n6+6t0/Qba9/EHSklIMHoOAAAADEJIO8hkMqn9B58q/ly0tv7zFaPnAAAAwCCEdA6UC31MDcf8Qfs+/kDntmwyeg4AAAAMQEjnUKvJU+VbqbJWjxmhlPh4o+cAAAAgjxHSOeTm7a0uM75R7JnT2jj+70bPAQAAQB4jpB9CcIswNfnL33Xwqy90avUqo+cAAAAgDxHSD6nFq5NUqk5d/fjMaN26ft3oOQAAAMgjhPRDsnh4qOtXs3Tr6hX99JdnjZ4DAACAPEJI54LARiEKfXmijn0/T0e/n2/0HAAAAOQBQjqXNPv7Swpq0kw//eWPSrhwweg5AAAAcDJCOpeYLRZ1+fIbpSUl6cc/jpbNZjN6EgAAAJyIkM5FpWrWUss33tGvq1fp0L9nGD0HAAAATkRI57KQZ55ThXYdtP4fL+j68WNGzwEAAICTENK5zGQ2q+uMb2Tx8NDKEYOVnpJi9CQAAAA4ASHtBN5ly6rTp1/p8v592vrPV4yeAwAAACcgpJ2keq/eajBqrHZPm6qzGyKNngMAAIBcRkg7UZt33lfJ6jX0w6hhvOohAABAIUNIO5FrsWLqPnOukq5c1tpnx/KUeAAAAIUIIe1kgSGPqMXEN3RiySJFffu10XMAAACQSwjpPND0hb+rfOu2Wv+353Xj5Amj5wAAACAXENJ5wGQ2q+uX38rFzU0rh/OUeAAAAIUBIZ1HigcHq9MnX+rSvj3aMvFlo+cAAADgIRHSeah6775qOPYZ7fnXuzr1w0qj5wAAAOAhENJ5rM0776t0/Qb6YcxwxZ87Z/QcAAAA5BAhnccsHh7qMXuB0m/f1soRg2VNSzN6EgAAAHKAkDaAX42a6jD9M53fulnb3/yn0XMAAACQA4S0Qeo88aTqDhupHe+8qTPrfzJ6DgAAABxESBuo/fvT5VezllaNHKLES5eMngMAAAAHENIGci1WTD1nL1BKbKxWPfWkbFar0ZMAAACQTYS0wfzr1lPb9z7U2ch12jn1LaPnAAAAIJsI6Xyg/sjRqjlgkLZNelVnN643eg4AAACygZDOB0wmkzp9MkMlq9fQymGDFH/+vNGTAAAA8DsI6XzCzdtbvb5bpNTERK0Y+rjSU1ONngQAAIAHIKTzkVK166jTJ18qZvtWbX55nNFzAAAA8ACEdD5Ta+AghTzzJ+2dPk3HFy80eg4AAAB+AyGdD7V++12VafaoVj89UtePHzN6DgAAAO6DkM6HXNzc1HPO97J4eGjZE/2Umpho9CQAAAD8D0I6nyoeHKzu33yna0cOa+1zT8tmsxk9CQAAAHchpPOxiu06qMXE13Vk3hz95/NPjJ4DAACAu2QrpNetW3fPbUuWLMn1MbhX8xfHq0q3Htrw4l90bstmo+cAAAAgg+VBd0ZGRiotLU1TpkyR1Wq1356WlqZp06apd+/eTh9Y1JnMZnX792zNadVcy4f015Ate+RTvrzRswAAAIq8B4b0kSNHtGPHDl27dk2zZs367xdZLBo1apTTx+EOd19fhS9Yorktm2nZoL4a9NNmWTw8jJ4FAABQpJls2fgrtjlz5mjIkCF5sSdbkpOTFRUVpXr16snd3d3oOXnm5IplWjogXHWfHK7OX3wtk8lk9CQAAIBC7UHdma1rpDt16qSffvpJkjR58mQNGzZMR48ezf2leKBqPXopdMJr+nn2N9r/6UdGzwEAACjSshXS48ePV3R0tLZv364dO3aod+/eeuONN5y9DfcROv4VVe0Rrg3/eEHRmzYYPQcAAKDIylZI37x5UyNGjNCmTZvUo0cP9e3bV7du3XL2NtyHyWxW16++Vclq1bV8yADFnT1r9CQAAIAiKVshnZqaqtTUVG3evFmPPfaYbt26paSkJGdvw29w9/FR+IIlSk9J0dLHeyuV/ywAAADyXLZCun379goNDVXJkiVVr149DRgwQD169HD2NjyAX42a6j5zri4f+I9Wjx0p211PTwgAAADny9azdkjSxYsXFRQUJEk6evSoatWq5dRhD1JUn7Xjfna/P1WbXv6HQl+eqMcmvGb0HAAAgELlQd35wOeRzmS1WrV8+XJt2rRJaWlpatGihapVqyaLJVtfDidq8sLfde3oYW1/85/yq1FLtQYOMnoSAABAkZCtSzvee+897dixQ8OHD9fIkSO1f/9+TZkyxdnbkA0mk0kdpn+mco+Fac3TI3Vh9y6jJwEAABQJ2QrpzZs367PPPlOHDh3UqVMnffrpp9q0aZOztyGbLO7u6jVvsYoFldHSgeGKP3fO6EkAAACFXrZC2mazydXV1f65m5tbls9hPK/SpdV70XKlJiZqyYBeSk1MNHoSAABAoZatkK5Vq5YmT56ss2fP6uzZs5o8ebJq1Kjh7G1wkH+duuoxa76uHDygH0YN45k8AAAAnChbIT1x4kTFxcVp0KBBGjhwoG7cuKFXXnnF2duQA5U7d1Xrt9/TiaWLtfWf/GcEAADgLA8M6ZSUFI0bN047duzQ22+/rW3btqlBgwZycXGRt7d3Xm2Egx557s+q/9QY7ZwyWT/P+dboOQAAAIXSA0P6ww8/VEJCgkJCQuy3vf7664qLi9P06dOdPg45YzKZ1H7aRyrfuq1+fGa0zm6INHoSAABAofPAkN6wYYPee+89lSpVyn5bYGCgpkyZonXr1jl9HHLOxc1NveYtVslq1bVsUF9dPfyz0ZMAAAAKlQeGtKurqzw8PO653dvbW25ubk4bhdzhUaKE+i75QRZPLy0O76qEmBijJwEAABQaDwxps9mshISEe25PSEhQWlqa00Yh9/hUqKA+ESt1+8Z1RfTroZT7/OcJAAAAxz0wpHv06KEJEyYoKSnJfltSUpImTJigTp06OX0cckdgoxD1nPO9rhw6qBVPDpSV/xIEAADw0B4Y0sOHD1fx4sXVokULDRw4UP3791eLFi3k4+OjZ599Nq82IhdU7txVHT74RL+u+UE//eVZ2Ww2oycBAAAUaJYH3Wk2m/X666/r6aef1uHDh2U2m1W/fn0FBgbm1T7kogajxiru7BntnDJZPhUrq/mLLxk9CQAAoMB6YEhnCg4OVnBwsLO3IA+0eO0NxZ45rS2vjpdP+QqqPWiw0ZMAAAAKpGyFNAoPk8mkzp//W4kXYrR67Ah5li6tSu07Gj0LAACgwMnWS4SjcLG4u6vX/AiVqlVbyx7vo4t7dhs9CQAAoMAhpIsojxIl1HfpanmVDtDiPt10/fgxoycBAAAUKIR0EeZdpoz6rfhRJrNZC3t0Uvz580ZPAgAAKDCceo30sGHDdO3aNVksd37MpEmT1LBhQ/v948eP1969e+Xp6SlJeu6559SxI9fr5qWSVaup79LVWtCptRb16qzH126Sp5+f0bMAAADyPaeFtM1m06lTp7RhwwZ7SP+vqKgozZ49WwEBAc6agWwIbBSi8O+XanGvLlrSr6f6r1wrVy8vo2cBAADka067tOPUqVMymUwaM2aMevXqpdmzZ2e5PykpSTExMXrllVfUs2dPffjhh7Jarc6ag99RoXVbdZs5VzE7t2vFkwOVnppq9CQAAIB8zWkhHRcXp9DQUH388ceaOXOm5s2bp61bt9rvv3btmh599FFNnjxZCxYs0J49e7Rw4UJnzUE21OjTTx0+/FSnflipH58ZLRv/xQYAAOA3ubz22muvOeMblylTRh07dpSrq6s8PT2VkpKiqKgotWzZUpLk6+ur7t27y8vLS66urvL29taaNWvUvXv33/3e6enpunz5sgICAn7zshHkTNAjTWS2WLRv+r90+8YNVerURSaTyehZAAAAhnhQdzqtQvfs2aPU1FSFhoZKunPN9N0//NixYzp9+rQ6d+583/thnObjXtbtmze194P35Fa8uML++abRkwAAAPIdp13aER8frylTpig5OVkJCQmKiIjI8owcNptNkydPVmxsrFJTUzV//nyesSOfMJlMav3WVDUY/bR2TpmsnVMmGz0JAAAg33HaEXDbtm114MAB9e7dW1arVYMHD1ZISIjCw8P1xRdfqFatWho7dqyeeOIJpaWlqVOnTurRo4ez5sBBJpNJHT74RKmJidoy8WW5FvPWI88+b/QsAACAfMNks9lsRo9wVHJysqKiolSvXj25u7sbPadQs6alafmQgTq5LEKdPv1S9UeMMnoSAABAnnlQd/LKhnggs8Wi7t9+p0qduujHP47RkfnfGT0JAAAgXyCk8bss7u7q9d0iBYe10g+jhurk8qVGTwIAADAcIY1scfXyUp9FyxUY0lgrnhyo02vXGD0JAADAUIQ0ss2teHH1XfqD/GrV1tKBvXX6p7VGTwIAADAMIQ2HePr5qf/KdSpZvYaW9u+lM5HrjJ4EAABgCEIaDvPy91f/VT+pRLXqWtKvp86s/8noSQAAAHmOkEaOePn7a8BdMX12Q6TRkwAAAPIUIY0c8ypd+k5MV6mqiL49dHbjeqMnAQAA5BlCGg8lM6Z9K1dRRJ/uit60wehJAAAAeYKQxkPzCgjQwB8i5Vupshb36a7ozRuNngQAAOB0hDRyhVdAgAb8ECnfipW0OLwrz+YBAAAKPUIauaZYYKAGrl6vktWqK6JvD/2yaoXRkwAAAJyGkEau8goI0IDV6+Vft76WPd5HxxcvNHoSAACAUxDSyHWefn4asGqdgpo214qhj+vwd7ONngQAAJDrCGk4hbuvr/otW63yrdroh1HDdPDrL42eBAAAkKsIaTiNm7e3ei9eocqdumjtH8do3yfTjZ4EAACQawhpOJWrp6d6zY9QtV59tP5vz2vXe1OMngQAAJArCAv2zq8AACAASURBVGk4ncXdXT1mz1etgU9o84Rx2vzq/8lmsxk9CwAA4KFYjB6AosHF1VVd/z1Lbj4+2jX1Ld26dlUdPvxUZhcXo6cBAADkCCGNPGN2cVGHDz+VZyl/7XznTd2+fl3dZs6Rxd3d6GkAAAAO49IO5CmTyaSw195Qm3fe14klixTRp7tS4uONngUAAOAwQhqGaPz8C+ry5TeK3rRBC7q0U9LVq0ZPAgAAcAghDcPUHTJM4fMjdO1wlOa1D1NcdLTRkwAAALKNkIahqnbvqX7L1yjx4gXNa9dC144eMXoSAABAthDSMFxwWCs9/uNGpaemaF67Fjq3ZbPRkwAAAH4XIY18IaBhIw3esF2epQO0sEdHHVv0vdGTAAAAHoiQRr7hW6mynojcqsCQxlox9HHt/XCa0ZMAAAB+EyGNfMWzVCn1X7VO1Xv10YZxf9X6F1+QzWo1ehYAAMA9CGnkO66enuoxZ4FC/vi89n30L6148nGl3b5t9CwAAIAseGVD5EtmFxe1ffdf8qlQURtf+psSL11U+PdL5ennZ/Q0AAAASZxIIx8zmUxq8ue/qvu383Rxzy591yZUN06eMHoWAACAJEIaBUCtAY+r/8p1unX9mua2flTRmzcaPQkAAICQRsEQHNZSQzbtlFfpAC3s3lFR335t9CQAAFDEEdIoMEpUqaonNmxX+VZttObpp7Tp5XE8owcAADAMIY0CxaNECfWJWKmGY/6g3e9P0bJB/ZSamGj0LAAAUAQR0ihwXFxd1f6DT9T23Q/0y8plmtehpeLPnTN6FgAAKGIIaRRIJpNJjzz7vHovWq6bv5zUnJbNdHHvHqNnAQCAIoSQRoFWpUs3DYrcKhc3N83v0FKH584yehIAACgiCGkUeKXr1deQLbtVptmj+mHUMG34x19lTUszehYAACjkCGkUCl6lS6vfih8V8sfntXf6NC3q2VlJV68aPQsAABRihDQKDRdXV7V77wN1/uJrnd++VXPCmurywQNGzwIAAIUUIY1Cp97QEXp87SZZU1P1XZtQHf1+vtGTAABAIURIo1Aq07SZnty6RwENQ7Ry2CBtmvCSrOnpRs8CAACFCCGNQqtYUJAGrlmvBqOf1u733tHi8K5KunLF6FkAAKCQIKRRqLm4uanj9M/U8ZMZOrdlk2aFPqKYHduNngUAAAoBQhpFQoORo/XE+m1ycXXV/I6ttO/jD2Wz2YyeBQAACjBCGkVGYMgjenLbXlXq3FXr//5nrRg6SCnx8UbPAgAABRQhjSLFo2RJ9V6wRC1ff1snIhZqdlhTXT38s9GzAABAAURIo8gxmc1q9vdxGvDDT0qOvak5LZvpyHdzjJ4FAAAKGEIaRVb5Vm00dPt+BYY01qqnntTa555WalKS0bMAAEABQUijSPMuU0YDV0eq6d/G6eBXX2hOy2Zc6gEAALKFkEaRZ7ZY1OqNt9Vv+RrdunpFc1o00cGvvuBZPQAAwAMR0kCGSh06adjOAyrXoqXWPve0Vjz5uG7fvGn0LAAAkE8R0sBdigUFqd+y1Wr5xjs6uSxCsx4NUczOHUbPAgAA+RAhDfwPk9msZn/7hx5ft1mSNK99mHZOfVs2q9XgZQAAID8hpIHfULb5oxq6Y7+qh/fVllfH6/tuHRQXHW30LAAAkE8Q0sADeJQooR6z56vTp1/q4p5d+rZpfR2ZN9foWQAAIB8gpIHfYTKZVH/EKA3bdUB+tepo1cghWjHsCd2+ccPoaQAAwECENJBNJapU1aB1m9Ri4us6EbFQ3zRtoDPrfzJ6FgAAMAghDTjAbLHo0Zcm6In12+Tq5aWF3Tpowz/+qrTbt42eBgAA8hghDeRAUJOmGrp9nxqOfUZ7p0/TnLCmuvSf/UbPAgAAeYiQBnLItVgxdfjgE/Vdskq3rl3V3JbNtPX1iUpPSTF6GgAAyAOENPCQKnfuquF7f1bNAYO0Y/IkTqcBACgiCGkgF3j6+anbv2cp/PulSrpymdNpAACKAEIayEXVevTidBoAgCKCkAZyGafTAAAUDYQ04CSZp9O1Bj6hHZMnafZjjXVh106jZwEAgFxCSANO5Onnp65ffavei5br9s2bmtsmVJF/fV4p8fFGTwMAAA+JkAbyQNVuPTRi388K+cNz2v/ZR/o6pI5Orlhm9CwAAPAQCGkgj7j7+Kjd+x9q8Ibt8ihZUksHhGvZE/2VEBNj9DQAAJADhDSQx8o0a64nt+1V2KS39Ovqlfo6pLYOzPhMNqvV6GkAAMABhDRgABdXVzV/8SUN23NIQY2bat3zz2he+5a6+nOU0dMAAEA2EdKAgUpWrab+K9eqy5ff6PqJY/q2eSNtGPc3JcfFGT0NAAD8DkIaMJjJZFLdIcP01IFjqj9ytPZOn6avG9bSkfnfyWazGT0PAAD8BkIayCc8S5VSx+mfacimnfIuW06rRgzW913a6dqRw0ZPAwAA90FIA/lMUJOmGrxphzpM/0xXDh3Qt80aauP4F3nuaQAA8hlCGsiHzC4uajj6aY08eFx1nhyuPf96V183qq2j38/ncg8AAPIJQhrIx7z8/dX50y/1xIbt8goI0MphgzS/Qytd2rfX6GkAABR5hDRQAJRt/qiGbNmtjh9/oesnjml2WFOtfvopJVy4YPQ0AACKLEIaKCDMLi5q8NQYjTp0Qk3+8ncd+W62/l2/unZOmay027eNngcAQJHj1JAeNmyYunfvrvDwcIWHh+vAgQNZ7t+2bZt69uypTp06adq0ac6cAhQa7r6+aj15ikbsP6yK7Tpqy8SX9XWj2jq+eCHXTwMAkIcszvrGNptNp06d0oYNG2Sx3Ptjbt++rf/7v//TrFmzVKZMGT399NPauHGjWrdu7axJQKFSsmo1hS+I0NkNkdrwjxe0fMgABYe1Uuu331NQ4yZGzwMAoNBz2on0qVOnZDKZNGbMGPXq1UuzZ8/Ocv/BgwdVsWJFlS9fXhaLRT179tTq1audNQcotCq0aacnt+9Tx48+17VjRzQnrKlWDB2km6d+MXoaAACFmtNCOi4uTqGhofr44481c+ZMzZs3T1u3brXff/nyZZUuXdr+eUBAgC5duuSsOUChZnZxUYNRYzUq6qQefWmCflm1XF83qq3Ivz6vpCtXjJ4HAECh5LSQDgkJ0ZQpU+Tl5SU/Pz/1799fGzdutN9/v2s5TSaTs+YARYK7j49aTHxdo6JOqt6wkfrPF5/oq7pVteOdN5WamGj0PAAAChWnhfSePXu0fft2++c2my3LtdKBgYG6evWq/fPLly8rICDAWXOAIsW7TBl1/OhzDd8bpQpt2mvraxP0Vb3qOvjvGbKmpRk9DwCAQsFpIR0fH68pU6YoOTlZCQkJioiIUMeOHe33N2zYUL/++qvOnDmj9PR0rVixQq1atXLWHKBIKlWzlsIXRGjQT1vkW6my1j47Vt80qa8TSyN4hg8AAB6S00K6bdu2at26tXr37q1+/fqpX79+CgkJUXh4uC5duiR3d3e9/fbb+tOf/qRu3bqpSpUq6tKli7PmAEVaucdaaFDkFvWaHyFJWjaor2a3aKJTq1cR1AAA5JDJVgD/r2hycrKioqJUr149ubu7Gz0HKFCsaWk6Mm+Otr/5T8We/lVlmocq7LU3VKFNO6OnAQCQ7zyoO3llQ6CIMVssqvvkcI08cFQdpn+m+HPR+r5rey3o3Fbnt239/W8AAAAkEdJAkeXi5qaGo5/WqKgTavvuB7p27IjmtQ/TovCuurh3j9HzAADI9whpoIizeHjokWef1+iff1HLN97RxT27NCesqSL699LFPbuNngcAQL5FSAOQJLkWK6Zmf/uHRh/5VY+9Okkx27ZoTstmWtSrC5d8AABwH4Q0gCzcfXwUOv4VjT56WmGT3tKl/Xs1r32YFnRpp7Mb1/MsHwAAZCCkAdyXu4+Pmr/4ksYcPa3Wb7+n68eO6Psu7TSvfUv9+uNqghoAUOQR0gAeyLVYMTX58181+sivajftI8VHn9Xi8K6a27K5Ti5fKpvVavREAAAMQUgDyBaLh4dC/vCsRv18Uh0//kK3rl3V0oG9NfORujr0zb+Vlpxs9EQAAPIUIQ3AIS5ubmrw1Bg9dei4us2cKxcPD/34h1H6slZl7XpvipJjY42eCABAniCkAeSI2WJR7cef0NDt+9RvxY8qVaeuNk8Ypy9qVNCml8cpISbG6IkAADgVIQ3goZhMJlVq31EDVq7Vk9v2qnLnbtrzr3c1o1YlrfnDKF07esToiQAAOAUhDSDXBIY8oh7ffqenok6owVNjdXTBd5oZUkcR/XrqTOQ6nukDAFCoENIAcl2JylXU/l8facyxMwp9eaIu7tmlhd076psm9XXw3zOUmpRk9EQAAB4aIQ3AabxKl9ZjE17TmONn1WXGTJldXbX22bH6onp5bX71/xR/7pzREwEAyDFCGoDTWdzdVffJ4Rq6fZ8eX7tR5Vu20e733tGMWpW0YuggxezcYfREAAAcRkgDyDMmk0nBYa3Ua94ijTr8ix557i86vXa1vmsTqjktm+vw3FlKu33b6JkAAGQLIQ3AEL4VK6nN2+9q7MlzajftIyXHxeqHUcP0ebVgbRz/om6e+sXoiQAAPBAhDcBQbt7eCvnDsxr5nyMa8MNPKt+yjfZOn6av6lbTwp6ddXL5UlnT0oyeCQDAPSxGDwAA6c5lHxXatFOFNu2UEBOjQzO/1MGvvtDSgb3lXS5YDUaNVf0Ro+VdpozRUwEAkMSJNIB8yLtsWYX+36sac+y0es1brFK1amvbpFc1o0YFLR88QKfXrpE1Pd3omQCAIo4TaQD5ltliUfXwPqoe3kc3Tp7QgS8/18+zvtbxiIUqHlxedYeNVL1hI+VbsZLRUwEARZDJVgBfaiw5OVlRUVGqV6+e3N3djZ4DIA+lJSfrl+VLdeibr3Tmp7WSpApt26v+8FGq1qu3LB4eBi8EABQmD+pOQhpAgRV35oyiZs/Uz99+rbizZ+Th56fag55U/RGjVLp+A6PnAQAKAUIaQKFms1p1Zv1Pipr5lU4ui1B6SooCH2miukNHqGb/x+Xl72/0RABAAfWg7uSPDQEUeCazWZXad1SPWfP09KkYtX33A1nTUhX5wnP6vHIZLRkQruOLF/JiLwCAXMWJNIBC68qhgzo8d5aOzJujxIsX5F6ihGr2G6jaTwxVucdayGQyGT0RAJDPcWkHgCLNmp6usxsidXjOtzqxdLHSkpLkW6myaj/xpOoMHqqS1aobPREAkE8R0gCQISUhQSeXRejw3Fk6E7lOstkU1KSZag0YpBr9Bqp4uXJGTwQA5COENADcR/z58zo6f66Ofv+dLv9nv2QyqdxjYXeiuk9/eQUEGD0RAGAwQhoAfsf1E8d1bOF8Hft+nq4dOSyT2azybdqpZv/HVT28rzz9/IyeCAAwACENAA64+nOUjn4/T8cWztfNX07KbLGoYodOqtn/cVXrES53X1+jJwIA8gghDQA5YLPZdHn/Ph1dOF/HFs5XfPRZubi5qUK7Dqoe3ldVu/eSV+nSRs8EADgRIQ0AD8lmterCrp06HrFQJ5YuVtyZ0zKZzQoOa6Vq4X1VrWdv+ZQvb/RMAEAuI6QBIBfZbDZdPvAfnVwWoRNLF+va4Z8lSUFNmql6eF9VC+8jv+o1DF4JAMgNhDQAONH148d0YmmETi5drIt7d0uS/OvWU7WevVWlW08FNW4ik5kXkgWAgoiQBoA8Enf2rE4uX6ITSxbp/LYtslmt8goMVJUu3VWlW09VbNdBbt7eRs8EAGQTIQ0ABrh17ZpO/7hav6xartNrVys5NlYu7u4q37qtqnbrqSpde8inQgWjZwIAHoCQBgCDpaem6vy2LTq1crl+WbVcN385KUkqXb+BqmREdVCTpjK7uBi8FABwN0IaAPIRm82mGyeO65eVy3Vq1XKd375VtvR0eZQqpYrtOqpypy6q2L6TvMuUMXoqABR5hDQA5GO3rl/X6R9X6/S6NTq9bo2SLl2SJJVu0FCVOnZR5U5dVPbRx+Ti5mbwUgAoeghpACggbFarrhw6qF9/XK3Ta1crZvtWWdPS5OrtrQpt2qlSh86q1KmLSlSuYvRUACgSCGkAKKCS4+IUvXG9Tq9bo1/X/KC4M6clSSWqVFWFtu1VoU17lW/dlldYBAAnIaQBoBCw2Wy6cfKETv+4WmfWr9O5TRuUEh8v6c5lIBVat1OFtu0VHNZKbsWLG7wWAAoHQhoACiFrWpou7t2jsxt+UvSGSJ3fvlXpyckyWywKatIs48S6nco0D5WF/10JADlCSANAEZB665ZidmzT2fV3wvri3t2yWa2yeHqqbGgLlW/ZWsFhrRTUpJksHh5GzwWAAuFB3WkxaBMAIJe5enqqYtv2qti2vSQpOTZW0Zs3KnpDpM5ujNTWf74iSXJxc1NQ0+YKDmul4LBWKts8lEtBACAHOJEGgCLi1vXritm+Vee2bNK5LZt0af9e2dLTZXJxUWCjR1QuI6zLPRYmTz8/o+cCQL7ApR0AgHukJCQoZud2nc8I6wu7dyo9OVmS5F+vvsq1aKmyzUNV9tHH5Fupskwmk8GLASDvEdIAgN+Vdvu2Lu7ZrXNbN+nc5o2K2bldqQkJkiSvgACVbf6YymSEdeAjjeXq6WnwYgBwPkIaAOAwa3q6rh3+WTE7tilm53bF7Nimm7+clCSZXV0V0DDEfmJdpnmofMqXN3gxAOQ+QhoAkCuSrlxRzM7tupAR1hf37lbarVuSJO9ywSrTtLmCGjdVUNNmCgxpLHcfH4MXA8DD4Vk7AAC5wqt0aVXr0UvVevSSJKWnpurKwQP2E+uLe3bpxJJFdx5sMsmvRk0FNW6qwMZNFdS4qQIaNuKp9wAUGpxIAwBy1a1r13Rp3x5d2LNLF/fu1qW9u5V48aIkyWyxyL9+gzun1hlvpWrXkdnCuQ6A/IlLOwAAhrHZbEo4f14XM8L64t7durRvj5JjYyVJFk9Pla7XQAGNQhTQ8M6bf736nFwDyBcIaQBAvmKzWnXjl5O6uGeXLu3do8sH9uvywf8oJS5OkmRycVGp2nXsYR3QKEQBDRrJ3dfX4OUAihpCGgCQ79msVsWe/lWX/7P/TlhnvGVeFiJJvpWr/DesG4bIv259FQ8O5jmuATgNf2wIAMj3TGazSlSpqhJVqqpG3/722xMvXvxvWGdEtv0PGiW5lygh/zr15F+vvvzr3nkrXa8+p9cAnI6QBgDka8WCglQ5qKsqd+5qvy05NlZXDh3U1Z8P6erPh3Ql6pCOzJtjvzREkooHl7fHdem69eVfv4H8atSUi5ubEf8MAIUQIQ0AKHDcfX0VHNZSwWEt7bfZbDbFnz2rKxlxfTXqzvsz636UNS1N0p1nDSlZo6b869STX63aKlWrjkrVqq0S1arLwqWCABxESAMACgWTySSfihXlU7GiqnbrYb89PSVF148fs4f11Z8P6eKeXTq2aIGU8WdCJhcXlahcRX4ZYe1Xq7ZK1awtv5q15Fa8uFH/JAD5HCENACjUXNzcVLreneum75aalKTrx4/p+tEjun7siK5lvP919Ur7CbZ05xKRzLAuVbuO/GrWUslqNeQVGMgfOQJFHCENACiSXL28FNgoRIGNQrLcnp6aqpunfskS2NeOHtbBr2coLSnJ/ji34sVVolp1laxWQyWrVVfJ6jXsH3uULJnX/xwABiCkAQC4i4urq0rVrKVSNWtJ6mO/3Wa1Kj46WtePH9WNkyd048Rx3Th5XBf37NLxRQtks1rtj/X091eJqtXlV73Gf2O7eg2VrFpNrsWKGfCvAuAMhDQAANlgMpvt12BX6tg5y31pycmK/fWUPbBv/nLn/Zmf1urn2d9keax3mbLyrVzF/laiSlX5VqqiEpWrcLkIUMAQ0gAAPCSLu7tK1aqtUrVq33NfSkKCbv5y0n6CffPUL4r99ZTObohUwpxvs34fLy+VyIzsSneFduUq8q1YiZdNB/IZQhoAACdy8/ZWQMNGCmjY6J770m7fVuyZ04r99ZT97eavpxR7+pTORK7Lck22JHmXLWeP6uLlK8inQkX7W/HyFeTq6ZlX/ywAIqQBADCMxcPjruuxs7LZbEq6fPm/gX36v7F9bssmxZ8/J1t6epav8QoIkE/5ivdEduabe4kSXDoC5CJCGgCAfMhkMqlYYKCKBQaq7KOh99xvTUtTQkyM4s6eUVz0mTvvM96uHo7Sr6tXKu327Sxf41a8eJbILl4uWN5ly8m7XLD9Yzdv77z6JwIFHiENAEABZLZY5FOhgnwqVJDU8p77bTabbl25kiWw46LP2sP7ws7tun3jxj1f516ihLzLlrsT1pmBXS5Yxe8Kbk62gTsIaQAACiGTySSvgAB5BQQoqEnT+z4mNSlJCRdilHD+nOLPn1P8uXNKiDlv//zKoQNKvHTJ/gqQmSxeXvYT7OLlglUsqMxdb0EqFlRG3kFleFVIFHqENAAARZSrl5dKVq2mklWr/eZj0lNTlXjhguLPn7MHdkLMefvn0Zs3KunSRaWnpNz7/YsV+29gBwbZP/YuUybL7Z6lSslkNjvznwo4BSENAAB+k4ur612XkNyfzWbT7Rs3lHjxgv0t4cIFJV26qISMz68cOqDTa1crJT7+nq83u7rKKyBQ3kFl5BUUJK/SAVnfAv77sae/v8wW8gX5A/+TCAAAHorJZJKnn588/fzkX6fuAx+bmpioxEsXlXDhv9GdeOmi/eP4c9G6vG+vkq5cljUt7X4/TB5+fvIqHaBiAYHyvE9s3/25m48P13PDaQhpAACQZ1yLFVOJKlVVokrVBz7OZrMp+eZNJV25rKTLlzPeX7rz/q7brhw6oFtXLt/3DyclycXNTZ6l/OVRqpQ8S/nL06+UPP395eGX8XmpUlk+9izlT3wj2whpAACQ75hMJnmULCmPkiXlV6Pm7z4+PSVFt65ezRrcGbF969pV3bp2TbeuXdXVw1G6de2qbl+/LpvVet/vZbZY5OHndyfA/yey73x+52P3Enf2eZQoKfeSJXlBnCKIkAYAAAWei5ubvMuWlXfZstl6vM1qVXJsbJbIvn39WtaPr17VrevXdOPkcV3Ydec+a2rqb29wd5dHyZJ3AjsjsjM/di95n9tKlLDfZvHy4hS8ACKkAQBAkWMym+0n3iWrVc/W19hsNqXEx9sj+/bNG7p944aSb97I+nHG+4QLMbp6+Gcl37yh5NjYB35vFzc3uZcokSXC3Xx85e7rK7fiPnL39ZW7j6/cfHzk/j+3Zz7OxdU1N341cAAhDQAAkA0mk0nuPj5y9/GRb6XKDn2tNT1dybGx9tC+ffOGkm/cuCfGM29LunJZN06eUHJcrFLi4pSenPy7P8Pi4SG3zOC+T3y7+frKvbiP/THuvr5y8y4ut+LF5ertbf/Yxc0tp7+iIoeQBgAAcDKzi4v9mU1yIi05WSmxsUqOj7O/T46NVUpcrJLj4u68j41VSsbtmQGeeOmi/faUuLjsbXV1vRPXxbzlVry43Ip5yzXj/f9Gd+Zj7I/19par9533bt53HutarFihvWyFkAYAAMjnLO7usmS8UmVO2axWpcTHZw3vhHj9f3v3HhRV3cdx/LPAKiKPGorGlJdSzEyzZkwjDQQlL+CYl5kuTulYluVk2h+Jito0KkKMlGNNkuYl/UMN8sIQk45RCoyYUyM+E2aNYhqKiRost8Pye/4wdySgR1ZwAd+vf9j9nbOH7/qdL37mcNhjlZaqqrREVaWlskpLVFVy0+O/t1mlpSoruuja1yotVXVFxa19Y5vtesDueD1U2zt2lN3vH19veuxTz1o7f3/dE/yQ/IOC3H7/zaHZg3R8fLyuXLmi1atX11rfvXu3EhMT1bVrV0nSqFGjtGDBguYuBwAA4K5k8/K6frlH586Set728ZyW9Xewrhu6XV9LSlTlKJVVUnJ9zeGQVeaQ5XCoqqREjosXaq1ZDkedW9Lf0OXBvnrlv7/edt1NqVmDdE5Ojr766iuNGjWqzra8vDzFxMQoOjq6OUsAAABAM/C22+X99x9sNhVjjKorKmQ5HKq+OWCXOfSfng3fXdNTmi1IX716VUlJSZozZ47y8/PrbM/Ly1NBQYGSk5PVv39/LV26VJ07d26ucgAAANDC2Ww22Tt0uP6Z3N26ebqc/8uruQ68bNkyLViwQJ06dap3e2BgoN566y3t2bNHQUFBev/995urFAAAAKDJNUuQ3rVrl4KCghQSEtLgPh9//LGGDBkim82mV199Vd9//31zlAIAAAA0i2YJ0unp6crKytKkSZO0du1aHTx4UKtWrXJtLykp0ebNm13PjTHy8eEDRAAAANB6NEt63bRpk+txamqqcnNztXjxYtean5+fNmzYoMcff1xDhgzRtm3bFBkZ2RylAAAAAM3ijp4GXrJkiSIiIjR69Gh9+OGHeu+991RRUaE+ffooISHhTpYCAAAA3BabMQ18WF8LVllZqRMnTmjQoEFq3769p8sBAABAG/VvubPZPrUDAAAAaMsI0gAAAIAbCNIAAACAGwjSAAAAgBsI0gAAAIAbCNIAAACAGwjSAAAAgBsI0gAAAIAbCNIAAACAGwjSAAAAgBt8PF2AO27c1byqqsrDlQAAAKAtu5E3b+TPm7XKIG1ZliTpl19+8XAlAAAAuBtYliVfX99aazZTX7xu4WpqauRwOGS322Wz2TxdDgAAANooY4wsy1LHjh3l5VX7quhWGaQBAAAAT+OPDQEAAAA3EKQBAAAANxCkAQAAADcQpAEAAAA3EKQBAAAANxCkAQAAADcQpAEAAAA3EKQBAAAANxCkG2Hfvn2aMGGCIiMjtX37dk+Xg9u0bt06RUVFKSoqSgkJCZKk7OxsTZw4Uc8884ySkpJc+/7888+aOnWqxo4dqyVLlqi6utpTZcMN8fHxiomJkdRwL//44w9Nnz5dDOagRAAACNBJREFU48aN0xtvvCGHw+HJktEIBw8e1JQpUzRu3DitWLFCErPcFu3Zs8f1Mzs+Pl4S89yWlJaWKjo6WufOnZPU+Bn2WM8NbsmFCxdMeHi4uXLlinE4HGbixInm1KlTni4LbsrKyjLPPfecqaysNFVVVebll182+/btM2FhYebs2bPGsiwza9Ysk5mZaYwxJioqyvz444/GGGMWLVpktm/f7sny0QjZ2dlm+PDhZuHChcaYhnv52muvmbS0NGOMMevWrTMJCQmeKRiNcvbsWTNy5EhTWFhoqqqqzAsvvGAyMzOZ5TamrKzMPPHEE+by5cvGsiwzbdo0k5WVxTy3ET/99JOJjo42jzzyiPn9999NeXl5o2fYUz3njPQtys7O1pNPPqkuXbrIz89PY8eOVUZGhqfLgpsCAwMVExOjdu3ayW63q2/fvjpz5ox69+6tnj17ysfHRxMnTlRGRobOnz+viooKPfbYY5KkKVOm0PtW4urVq0pKStKcOXMkqcFeWpalo0ePauzYsbXW0fLt379fEyZM0L333iu73a6kpCR16NCBWW5jnE6nampqVF5erurqalVXV8vHx4d5biN27typ5cuXq3v37pKk48ePN2qGPdlznzvyXdqAoqIiBQYGup53795dx48f92BFuB3BwcGux2fOnFF6erpeeumlOj2+ePFind4HBgbq4sWLd7ReuGfZsmVasGCBCgsLJdWd4xu9vHLlivz9/eXj41NrHS1fQUGB7Ha7XnnlFV26dEnh4eEKDg5mltsYf39/vf322xo/frx8fX01bNgw2e125rmNWLlyZa3n9WWuf5thT/acM9K3yBhTZ81ms3mgEjSlU6dOadasWVq4cKF69epVZ7vNZqP3rdSuXbsUFBSkkJAQ11pDvaTHrZfT6VROTo4++OAD7dy5U3l5ea5rLG9Gn1u3/Px8paSk6Ntvv9Xhw4fl5eWlrKysOvvR57ahsT+rPdlzzkjfoh49euiHH35wPS8qKnL9CgKt07FjxzRv3jwtXrxYUVFRys3N1Z9//unafqPHPXr0qLV+6dIlet8KpKen69KlS5o0aZKuXbumsrIy2Wy2ensZEBCg0tJSOZ1OeXt70+NWpFu3bgoJCVFAQIAkafTo0crIyJC3t7drH2a59Tt8+LBCQkLUtWtXSdd/db9x40bmuY3656z+vxn2ZM85I32LnnrqKeXk5Ki4uFjl5eX65ptvFBoa6umy4KbCwkLNnTtXiYmJioqKkiQNGTJEp0+fVkFBgZxOp9LS0hQaGqr77rtP7du317FjxyRJu3fvpvetwKZNm5SWlqY9e/Zo3rx5ioiIUFxcXL29tNvtGjp0qNLT02uto+ULDw/X4cOH9ddff8npdOrQoUMaN24cs9zGDBgwQNnZ2SorK5MxRgcPHtSwYcOY5zaqsf8fe7LnNlPf+XDUa9++fVq/fr0sy9K0adM0e/ZsT5cEN61YsUIpKSm1Lud4/vnn1adPH8XFxamyslJhYWFatGiRbDab8vPzFRsbK4fDoYEDByouLk7t2rXz4DtAY6Smpio3N1erV69usJfnz59XTEyMLl++rKCgIK1Zs0adO3f2dOm4BV9++aU2b94sy7I0YsQIxcbG6siRI8xyG5OcnKzU1FTZ7XYNHjxYy5cv1+nTp5nnNiQiIkJbt27V/fffr5ycnEbNsKd6TpAGAAAA3MClHQAAAIAbCNIAAACAGwjSAAAAgBsI0gAAAIAbCNIAAACAGwjSANCCREREKC8vT+vWrdOBAwea9NizZs1ScXGxJGn27Nn69ddfm/T4AHC34c6GANACHTlyRP369WvSY958S+XPPvusSY8NAHcjgjQAtDDfffedTpw4oYSEBHl7eyssLEyJiYk6evSonE6nBg4cqNjYWPn7+ysiIkKPPvqoTp48qXfeeUc+Pj5av369qqqqVFxcrGeffVbz58/XokWLJEkzZsxQcnKypk+fro8++kiDBw/Wjh079MUXX8jLy0vdunXT0qVL9cADDygmJkb+/v46efKkLly4oAcffFBr1qxRx44dtXbtWu3fv192u1333HOP4uLiuA0zgLsOl3YAQAsTFhamQYMG6d1331VkZKSSk5Pl7e2t1NRU7d27V927d1diYqJr/+DgYH399dcaM2aMPv/8c61evVqpqanasWOHkpOTVVxcrLi4OEnSli1bFBQU5HptTk6ONmzYoK1bt2rv3r2Kjo7W3LlzdeNeXSdOnNDGjRuVnp6uoqIiZWRkqLCwUFu2bFFKSopSU1M1YsQIHT9+/M7+IwFAC8AZaQBo4TIzM1VSUqLs7GxJkmVZ6tq1q2v70KFDJUk2m02ffvqpMjMzlZaWpt9++03GGJWXlzd47EOHDmnChAkKCAiQJE2ZMkUrV67UuXPnJElPP/206xba/fv317Vr19SjRw8NGDBAkydPVmhoqEJDQxUSEtIs7x0AWjKCNAC0cDU1NVq8eLHCwsIkSQ6HQ5WVla7tfn5+kqSysjJNnjxZY8aM0dChQzV16lQdOHDAdXa5PvVtM8aourpakuTr6+tat9lsMsbIy8tL27ZtU15ennJycrRq1SoNHz5csbGxTfJ+AaC14NIOAGiBvL29XWF25MiR2r59u6qqqlRTU6OlS5dqzZo1dV5TUFCg0tJSzZ8/XxEREcrNzXW95p/HvGHkyJFKT093fZpHSkqKunTpot69ezdYW35+vqKjo9W3b1+9/vrrmjlzpk6ePNlUbx0AWg3OSANACxQeHq74+HhZlqU333xT8fHxmjx5spxOpx5++GHFxMTUec1DDz2kUaNGafz48erUqZN69eqlfv36qaCgQL169VJkZKRefPFFffLJJ67XjBgxQjNnztSMGTNUU1OjgIAArV+/Xl5eDZ9nGTBggMaPH6+pU6fKz89Pvr6+nI0GcFeymX/7nR8AAACAenFpBwAAAOAGgjQAAADgBoI0AAAA4AaCNAAAAOAGgjQAAADgBoI0AAAA4AaCNAAAAOCG/wGeUkNnmSw5uwAAAABJRU5ErkJggg==\n"
     },
     "metadata": {}
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(12, 8))\n",
    "ax.plot(np.arange(iters), cost, 'r')\n",
    "ax.set_xlabel('Iterations')\n",
    "ax.set_ylabel('Cost')\n",
    "ax.set_title('Error vs Transing Epoch')\n",
    "plt.grid(None)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.9-final"
  },
  "orig_nbformat": 2,
  "kernelspec": {
   "name": "python36964bit993ec77479a3441f817fdc4955f087a8",
   "display_name": "Python 3.6.9 64-bit"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}